Controllability on sl(2, ℂ) with restricted controls

Victor Ayala; Rodolfo Ribeiro; Luiz A.B.San Martin

doi:10.1137/130943662

Controllability on sl(2, ℂ) with restricted controls

Victor Ayala
, Rodolfo Ribeiro
, Luiz A.B.San Martin

Universidad Católica del Norte
Universidade Estadual de Campinas

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper we study controllability of affine invariant control systems on the group Sl(2, C) with restricted controls. We develop a method based on the action of Sl(2, ℂ) on the sphere S² ≈ ℂ ∪ {∞} by Möbius functions. Some controllability results are proved. It is proved also that controllability with restricted controls is not a generic property, contrary to the case of unrestricted controls, as proved in the classic paper by Jurdjevic and Kupka.

Original language	English
Pages (from-to)	2548-2567
Number of pages	20
Journal	SIAM Journal on Control and Optimization
Volume	52
Issue number	4
DOIs	https://doi.org/10.1137/130943662
State	Published - 2014
Externally published	Yes

Keywords

Complex special linear group
Controllability
Restricted controls

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10.1137/130943662

Cite this

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title = "Controllability on sl(2, ℂ) with restricted controls",

abstract = "In this paper we study controllability of affine invariant control systems on the group Sl(2, C) with restricted controls. We develop a method based on the action of Sl(2, ℂ) on the sphere S2 ≈ ℂ ∪ \{∞\} by M{\"o}bius functions. Some controllability results are proved. It is proved also that controllability with restricted controls is not a generic property, contrary to the case of unrestricted controls, as proved in the classic paper by Jurdjevic and Kupka.",

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T1 - Controllability on sl(2, ℂ) with restricted controls

AU - Ayala, Victor

AU - Ribeiro, Rodolfo

AU - Martin, Luiz A.B.San

PY - 2014

Y1 - 2014

N2 - In this paper we study controllability of affine invariant control systems on the group Sl(2, C) with restricted controls. We develop a method based on the action of Sl(2, ℂ) on the sphere S2 ≈ ℂ ∪ {∞} by Möbius functions. Some controllability results are proved. It is proved also that controllability with restricted controls is not a generic property, contrary to the case of unrestricted controls, as proved in the classic paper by Jurdjevic and Kupka.

AB - In this paper we study controllability of affine invariant control systems on the group Sl(2, C) with restricted controls. We develop a method based on the action of Sl(2, ℂ) on the sphere S2 ≈ ℂ ∪ {∞} by Möbius functions. Some controllability results are proved. It is proved also that controllability with restricted controls is not a generic property, contrary to the case of unrestricted controls, as proved in the classic paper by Jurdjevic and Kupka.

KW - Complex special linear group

KW - Controllability

KW - Restricted controls

UR - https://www.scopus.com/pages/publications/84906818865

U2 - 10.1137/130943662

DO - 10.1137/130943662

M3 - Article

AN - SCOPUS:84906818865

SN - 0363-0129

VL - 52

SP - 2548

EP - 2567

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 4

ER -

Controllability on sl(2, ℂ) with restricted controls

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Keywords

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